|
|
A212280
|
|
G.f. A(x)=1/(1-F(x)), where F(F(x)) = (1 - sqrt(1-16*x))/8.
|
|
1
|
|
|
1, 1, 3, 17, 131, 1177, 11531, 119201, 1276771, 14015401, 156585211, 1772626673, 20275611347, 233912585849, 2718842818923, 31816917837377, 374657837729987, 4436890509548617
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
F(x) is the generating function of A213422.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = sum(m=1..n, T(n,m)) for n>0, where T(n,m)= 1 if n=m, otherwise = (m *4^(n-m) *binomial(2*n-m-1,n-1)/n - sum_{i=m+1..n-1} T(n,i)*T(i,m) )/2.
|
|
MAPLE
|
T := proc(n, m)
if n = m then
1 ;
else
m*4^(n-m)*binomial(2*n-m-1, n-1)/n ;
%-add(procname(n, i)*procname(i, m), i=m+1..n-1) ;
%/2 ;
end if;
end proc:
if n = 0 then
1
else
add(T(n, m), m=1..n) ;
end if;
|
|
MATHEMATICA
|
Clear[t]; t[n_, m_] := t[n, m] = 1/2*((m*4^(n-m)*Binomial[2*n-m-1, n-1]/n - Sum[ t[n, i]*t[i, m], {i, m+1, n-1}])); t[n_, n_] = 1; a[n_] := Sum[t[n, m], {m, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Feb 25 2013, from formula *)
|
|
PROG
|
(Maxima)
Solve(k):=block([Tmp, i, j], array(Tmp, k, k), for i:0 thru k do for j:0 thru k do Tmp[i, j]:a,
T(n, m):=if Tmp[n, m]=a then (if n=m then (Tmp[n, n]:1) else (Tmp[n, m]:(1/2*((m*4^(n-m)*binomial(2*n-m-1, n-1))/n-sum(T(n, i)*T(i, m), i, m+1, n-1))))) else Tmp[n, m], makelist(sum(T(j, i), i, 1, j), j, 1, k));
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|